Geometry and measures worksheet — GCSE Higher

1.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

2.A trapezium has vertices (0, 2), (4, 2), (3, 5) and (1, 5). It is rotated 180° about the point (2, 2), and the image is then translated by the vector (1, −5). Work out the coordinates of the image of (0, 2).

3.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

4.The perimeter of a square is 20 cm. Work out the area of the square.

5.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

6.A solid is built from centimetre cubes: a base layer of 2 rows of 3 cubes each (a 3 by 2 rectangle of cubes), with one extra cube placed on top of one corner cube of that base. Looking down from directly above (the plan view), how many squares are visible?

7.A skateboard ramp is designed so that a straight rail RT is tangent to a circular curve at the point T, and TC is a chord of the curve from T to another point C on the curve. A second rail continues straight through T on the other side, so that the two rails together form a straight line, and the angle between that second rail and the chord TC is 109°. A support point D is placed on the curve, on the major arc TC. Work out the size of angle TDC, the angle subtended by the chord TC at D.

8.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

9.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.

10.An enlargement with scale factor 5 maps the point (4, 1) to the point (12, 9). Which of these points is invariant (does not move) under this enlargement?

11.Two similar model cars have a length scale factor of 2 from the small model to the large model. Priya works out that the area scale factor is 2² = 4, and then says the volume scale factor must also be 4, since that is the number she just calculated. Is Priya correct?

12.Two similar triangular flower beds have lengths in the ratio 3 : 7. The area of the smaller bed is 45 m². Work out the area of the larger bed.

13.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.

14.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.